def A(lastn,mode):
## mode 0: print all factorizations for a(n). There might be other combinations possible, but the programm should always find the maximum number of them
## mode 1: mode 0 + print leftover factors which could not be included in a factorization triplet, quadruplet... etc. (factors building a factorization pair with a prime already sorted out)
## mode 2: print only n,a(n)
	n,a=0,[1]
	while n<lastn:
		i,s,v,factors=2,str(a.count(a[n]))+"x"+str(a[n]),a.count(a[n]),[]
		while i<a[n]**(0.5):
			j=a[n]//i
			if j==a[n]/i:
				for x in (x for x in a if (x==i and a.count(i)>a.count(j)+factors.count(i)) or (x==j and a.count(j)>a.count(i)+factors.count(j))):
					ii=2
					while ii<=(a[n]/x)**(0.5)+0.1:
						if (a[n]/x)//ii==(a[n]/x)/ii:
							factors.append(x)
							break
						ii+=1
				v,s=v+min(a.count(i),a.count(j)),s+", "+str(min(a.count(i),a.count(j)))+"x"+str(i)+"*"+str(j)
			i+=1
		if a[n]/i==i:
			sq=a.count(i)//2
			if sq>0: v,s=v+sq,s+", "+str(sq)+"x"+str(i)+"*"+str(i)
			if a.count(i)/2>sq and len(factors)>0: factors.append(i)
		st,sp,factoriz,nu,x="",[],[],[a[n]],[]
		if a[n]>7 and len(factors)>2:
			flist,r,q=list(set(factors[:])),0,[]
			x.append(len(flist)-1)
			while r>=0:
				if nu[r]/flist[x[r]]==int(nu[r]/flist[x[r]]) and q.count(flist[x[r]])<factors.count(flist[x[r]]):
					q.append(flist[x[r]])
					if nu[r]/flist[x[r]]==1:
						factoriz.append(q[:])
						q.pop(r)
						x[r]-=1
					else:
						r=r+1
						nu.append(nu[r-1]/flist[x[r-1]])
						x.append(x[r-1])
				else:
					x[r]-=1
				while x[r]<0:
					r-=1
					if r<0: break
					q.pop(r)
					nu.pop(r+1)
					x.pop(r+1)
					x[r]-=1
			if len(factoriz)>0:
				##print(factoriz)
				fz,f,q,r,x=[factoriz[:]],[factors[:]],[[]],0,[len(factoriz)-1],
				while r>=0:
					j,c=len(fz[r][x[r]])-1,int(f[r].count(fz[r][x[r]][0])/fz[r][x[r]].count(fz[r][x[r]][0]))
					while j>=1:
						c=min(c,int(f[r].count(fz[r][x[r]][j])/fz[r][x[r]].count(fz[r][x[r]][j])))
						j-=1
					if c>0:
						q.append(q[r][:])
						f.append(f[r][:])
						fz.append(fz[r][:])
						r+=1
						while c>0:
							q[r].append(fz[r-1][x[r-1]])
							k=len(fz[r-1][x[r-1]])-1
							while k>=0:
								f[r].remove(fz[r-1][x[r-1]][k])
								k-=1
							c-=1
						fz[r].remove(fz[r-1][x[r-1]])
						x.append(len(fz[r])-1)
					else:
						x[r]-=1
					while x[r]<0:
						r-=1
						if r<0: break
						fz.pop(r+1)
						f.pop(r+1)
						if len(q[r+1])>len(sp): sp=q[r+1][:]
						q.pop(r+1)
						x.pop(r+1)
						x[r]-=1
		a.append(v+len(sp))
		if a[n]<1000:
			s=" "+s
			if a[n]<100:
				s=" "+s
				if a[n]<10:
					s=" "+s
		if mode!=2:
			if len(sp)>0:
				si=len(sp)-1
				while si>-1:
					ssi=len(sp[si])-1
					sv=sp.count(sp[si])
					s+=", "+str(sv)+"x"
					while ssi>-1:
						if ssi>0: s+=str(sp[si][ssi])+"*"
						else: s+=str(sp[si][ssi])
						sf=0
						while sf<sv:
							factors.remove(sp[si][ssi])
							sf+=1
						ssi-=1
					si-=sv
			if mode==1 and len(factors)>0:
				si=0
				s+="    "+"("
				while si<len(factors):
					sv=factors.count(factors[si])
					if si==0: s+=str(sv)+"x"+str(factors[si])
					else: s+=", "+str(sv)+"x"+str(factors[si])
					si+=sv
				s+=")"
			print(str(n+1)+"   "+str(a[n])+" "+s)
		else: print(str(n+1)+" "+str(a[n]))
		n+=1
	return a